"ELI the ICE man" is a mnemonic for remembering E(voltage)L(leads, for an inductor)I(the current)
and I(current)C(leads, for a capacitor)E(the voltage)
Looking at the Inductor graphs, the first one shows a dc power supply being turned on across an inductor. The voltage rises almost instantaneously to the maximum voltage the supply is producing, the current asymptotically approaches the maximum current allowed by the lumped resistance of the circuit. The second graph shows an AC source tied across the inductor the current peaks lag the voltage peaks by an amount dependant on the frequency and the value of inductance of the inductor.
Looking at the Capacitor graphs, the first one shows a dc power supply being turned on across a capacitor. The current rises almost instantaneously to the maximum current allowed by the lumped resistance of the circuit, the voltage asymptotically approaches the maximum voltage the supply can produce. The second graph shows an AC source tied across the capacitor the voltage peaks lag the current peaks by an amount dependant on the frequency and the value of capacitance of the capacitor.