An auxiliary verb attached to the continuative form of a verb to mean 'begin to (do)'. In modern usage, 始める (はじめる) is more common; 初める (そめる) appears in older or literary forms.
彼は急に話を初めたので、皆が驚いた。
He suddenly began to speak, so everyone was surprised.
春になると庭の花が咲き初める。
When spring comes, the flowers in the garden begin to bloom.
授業は午後一時に始めます。／授業は午後一時に初めます（文語的）。
The class will start at 1 PM. (／文語/literary variant shown)