This work was composed several years after Beethoven's first collection of violin sonatas, Op. 12 (1797–98), and following his initial compositions of string quartets and symphonies. While Op. 23 adopted the common three-movement structure for violin sonatas of the time, Op. 24, unusually for Beethoven's violin sonatas, expanded to a four-movement structure, which might foreshadow the subsequent Op. 30, No. 2.

In contrast to Op. 12, which was a set of three pieces, Op. 23 and Op. 24 were initially conceived as a set of two pieces (Beethoven had already published his Piano Sonata Op. 14 as a set of two). This is suggested not only by the composition period but also by the presence of the number "23" on the title page of the first edition of Op. 24, and by the fact that both works were dedicated to the music patron Count Browne.

Currently, this sonata is popularly known by the nickname "Spring," but there is no evidence that the name originated with Beethoven, nor does the term appear in the first edition. According to Lockwood, it began to be called "Spring" around 1860, i.e., after Beethoven's death. Its origin is presumed to stem not from any words of the composer or biographical details, but rather from the work's approachable and amiable atmosphere.

First Movement

From the very beginning of the piece, it is clearly demonstrated that the violin initially carries the melodic line, indicating a duo sonata for obbligato violin and piano, entirely distinct from the "accompanied keyboard sonatas" of the preceding era.

Several points are noteworthy regarding its form.

• Firstly, although it is in Allegro sonata form, it reverses the typical characterization of a lively main theme and a lyrical secondary theme; instead, the main theme is graceful, and the secondary theme is vigorous.
• The second point is the relative weight of the development section and the coda. Both are of nearly equal length; while the development section is brief, consisting of simple repetitions of figures derived from the secondary theme, the coda centers on the opening melody of the main theme, thus making the two sections equivalent. This can be considered a tendency differing from the Mozart generation. The modulation via chromatic progression (F to F-sharp) upon entering the coda also creates a striking, awakening effect.

Second Movement

It is written in a relatively free form, to the extent that it seems inappropriate to force it into a specific formal mold. In the first half, the opening theme of the movement appears a total of four times, with both the piano and violin taking turns as the melodic voice; after an intervening musical idea, the original melody is varied from the third theme statement by the piano, and when the violin further varies the theme, it begins with a modulation to B-flat minor, gradually departing from the theme. Modulations continue using enharmonic equivalents, and upon finally returning to the tonic B-flat major, the sixteenth-note motive derived from the first measure of the opening theme melody is repeated. At the end of the movement, after the middle section where harmonies shift successively, the dominant and tonic chords of the main key are repeated, as if to emphasize the tonic.

From an instrumentation perspective, not only is the music formed by the violin alternating with the piano in playing the melody and by the exchange of short motives resembling a "dialogue" between the two instruments, but also the fact that the violin becomes the principal voice during the significant modulation to the minor key in the middle section demonstrates how crucial the violin part functions.

Third Movement

This is a Scherzo movement in compound ternary form, but contrary to convention, the first half of the Scherzo proper is marked "no repeat" (繰り返しなし). On the other hand, there is no "Senza replica" (no repeat) instruction for the da capo. The Trio is remarkably short at 16 measures, and its first half is extremely simple in construction, with the piano and violin largely concluding in parallel thirds over a dominant pedal point. This suggests that the main focus is not on elaborate form or harmony, but rather on the contrast in sound with the crisp Scherzo proper.

Fourth Movement

A rondo developed with a cheerful theme, seemingly forming a pair with the First Movement, which begins with a graceful theme. The reversal of the order in which the melody is carried (piano then violin) compared to the First Movement might be an attempt to balance the outer movements as a pair. It is also noteworthy that the melodic line of the rondo theme (half note → neighboring tone → descending figure) closely resembles the opening theme of the First Movement.

Focusing on the equality of piano and violin, while the piano precedes in carrying the melodic line in the rondo theme, the violin precedes in the episodes. In the D minor episode in the middle section, virtuosic triplets, similar to those found in concertos, appear in succession. Furthermore, when the rondo theme is presented by the piano, it is a piano solo at the beginning of the movement, but with each return to the piano part within the movement, the violin's involvement gradually increases. And finally, when the entire rondo theme appears at the very end, the violin varies the thematic melody against a background of light arpeggiated chords from the piano. Thus, in this series of thematic returns, a transformation in the roles of the two instruments within the theme can be observed.