The speaker is the very old man of the title (note that this is a companion poem to "Old Man," in which the speaker is 60 rather than 70). He's in a nostalgic mood, recalling what it was like to be a toddler, waddling from one "chair" to another in his mother's bedroom. The poem thus immediately sets up a juxtaposition between two stages of life: infancy and old age.
The speaker has lived a fairly long time, given the era in which the poem was written (70 seems a lot younger now than it would have in the 19th century!). When the speaker mentions his age—"some threescore years / And ten"—the enjambment in lines 1-2 effectively draws out the phrase, as if to emphasize the length of his life. Looking back 70-ish years, the speaker describes his younger self as a "helpless babe." In a way, this phrase foreshadows his current state; his old age is a kind of second childhood, a return to limited mobility and dependency on others.
As a toddler, the speaker was only just learning to walk (now he's pretty much immobile). He "toddled / From chair to chair about my mother's chamber" (that is, around her bedroom or living quarters). He was so small and unsteady that he had to pause and prop himself against furniture as he navigated the room. The enjambment between lines 2 and 3 makes the poem itself sound as if it's pausing a moment before moving on to the next thing. The caesuras around "a helpless babe" also contribute to this hesitant sound. As an infant, then, the speaker moved tentatively, but he was adventurous in exploring the unknown world.
These opening lines establish the poem's meter: iambic pentameter (five metrical feet per line, each with an unstressed-stressed syllabic pattern). Listen to the rhythm of line 1, for example:
I well | remem- | ber how | some three- | score years [...]
Unrhymed iambic pentameter is known as blank verse. It's an old and traditional form in English poetry, and it's often used in monologues (e.g., Shakespearean soliloquies), since it's thought to closely approximate the rhythms of spoken English. As a result, it's well suited to the brief monologue of this "Very Old Man."