An alliance is the core social and strategic unit in Last War: Survival - most of the game's biggest systems (Alliance Tech, territory control, Rallies, SvS, seasonal war content) only work well with organized alliance participation, so joining one early and staying active is one of the highest-value decisions a new player makes.
Alliance Tech is funded by member donations of resources or gems and unlocks passive, alliance-wide bonuses once enough has been contributed - donating regularly, even in small amounts, is one of the best low-effort ways to help your whole alliance grow faster, and it benefits you too since the bonuses apply to every member.
Cities and territory (the specifics vary by season - see each season's own guide) are typically captured and held by alliance members working together, producing resources or ranking points for as long as they're held. Communicate with your alliance before attacking or defending contested territory - uncoordinated action is one of the most common ways alliances lose ground they didn't need to.
If you're ever unsure what your alliance needs from you, ask your R4s or leader directly - most alliances would rather answer a question than have a member guess wrong and waste effort.