After a false start and an acrimonious campaign, Nigerians headed to the polls Saturday to vote in what is expected to be Africa’s largest-ever election, and will determine who governs the continent’s top economy and oil producer.

As the country awoke, explosions rocked the northern states of Borno and Yobe, as Islamist insurgents launched what appeared to be coordinated attacks on security forces. Meanwhile, in several states card readers designed to verify voters’ identities weren’t working, according to voters and electoral...