The word karim means generous, magnanimous, highly majestic and merciful etc. one who possesses the qualities like kindness, mercy, forgiveness, patience, magnanimity, generosity etc. fully is called Karim. And Allah, the Almighty is the only Creator and possessor of all these attributes fully. Hence, he is the only Karim. Thus, Allah Karim means Allah is magnanimous, highly majestic, generous and merciful.
Nothing can be compared with the mercy and bounties of Allah. He has created for us the sun, the moon, light and air, fire, water, tress, animals and everything. His bounties have no limit. We are living on His mercy, but we do not express gratefulness to Him even on enjoying all these bounties. Yet He does not punish us. This is His generosity and magnanimity.