Dickinson often wrote poems with succinct moral messages, and this poem immediately states its message in clear terms:
Success is counted sweetest
By those who ne'er succeed.
In other words, success is most valued and best appreciated by those who "ne'er" (never) have it. This is a paradox typical of Dickinson's poetry, with "success" meaning more the less that people enjoy it—and implying that having success makes it seem less significant.
The poem is deliberately general both here and throughout, allowing for the power of its main idea to feel like it can apply to almost any situation that involves success (and by extension the desire for success). For example, the opening two lines would seem apt if applied to situations as different as unrequited love or a soccer player's failure to win a long hoped-for trophy.
The first two lines are packed with sibilance:
Success is counted sweetest
By those who ne'er succeed.
On the one hand, this dense use of sound makes the opening lines, an example of an aphorism, all the more memorable—they feel quippy and witty in their delivery of this moral message. On a subtler level, the /s/ sounds are an important part of the poem's opening metaphor, of success as a kind of "sweet taste" most desired by those who never have it. The /s/ sounds create a kind of salivation in the mouth of the reader, suggestive of both the enjoyment of food (success) and the way in which the body creates saliva in anticipation of food (desire).
The enjambment between the two lines creates a sense of anticipation as the reader waits for the answer to the implicit question posed by the first line: who counts success sweetest? The next line delivers this answer, and then concludes with a strong end-stop—the clear pause suggesting the speaker's assuredness in the truth of this aphorism.
These lines also establish the poem's meter, which is iambic trimeter:
Success is counted sweetest
By those who ne'er succeed.
The first line has an extra unstressed syllable, creating a feminine ending; this may seem like a hiccup, but the speaker will actually repeat this same pattern almost exactly in every other line throughout the poem.