API is Application Programming Interface. This is solution your programmer with codes, will integrate onto your website for accepting online card payments.
if you are aiming at nigerian market, get interswitch and/or etranzact API and integrate it with your website. they are both free
if you intend to go worldwide then consider getting the API of Paypal (if you can) and other major credit card service providers
That was why he said you should either of the credit card processors API on your website, however if you want global payments, then PayPal API.