強いる（しいる） means to force or compel someone to do something against their will. It has a strong sense of coercion, so it is not used for mild pressure or casual persuasion.
You will often see it in the passive form 強いられる（しいられる）, meaning to be forced into a situation with no real choice. This often points to pressure from authority, society, or unavoidable circumstances.
It commonly pairs with abstract hardships, not simple physical actions. Useful patterns include 苦戦を強いられる（くせんをしいられる）, “be forced into a hard struggle,” and 選択を強いられる（せんたくをしいられる）, “be forced to make a choice.”
Formal / written tone. You will see 強いる（しいる） in news, essays, and literature. In everyday speech, 無理やり（むりやり）, “by force / against someone’s will,” is usually more natural.