Anything done severally is done separately or independently, like when your classmates are called severally, or one at a time, to come up and solve a math problem on the board.
The adverb severally isn't used very often in everyday speech — it's much more common in legal documents. For example, a judge may find three defendants severally liable, or individually obligated to pay for something. The opposite of this is being jointly liable, or responsible along with at least one other person. Severally comes from several, which originally meant "separate."