In principle an audio interface gives you conversion from an analog signal (e.g coming from a microphone) to a digital signal which your computer can process and the other way around to your headphones/speakers. Plus for the home recording grade interfaces you normally get microphone amplifiers since the volume coming from the mic is in most cases very low and need to be brought up.
The soundcard in the mac certainly does that, but is more meant to be used with headsets and for skype call quality. You might be able to use certain so called "dynamic microphones" like the shure sm58
directly with your laptops microphone input using adapters (from the XLR plug microphones come with) but I have not idea what the results will sound like. And because, if i remember correctly, the MacBook Air has a combined headphone/microphone jack, you would need to add another adapter to have headphones plugged in at the same time as the mic.
The thing with the condenser type of microphones borodog and darell suggested is, that unlike dynamic ones, they usually need "phantom power" sent trough the microphone cable. You laptop can't do that and those microphones will not work without the required electricity.
An USB-mic is essentially a normal mic with an simple audio interface built in so you can directly plug into an laptop or iphone/ipad.
There are also XLR-to-USB adapters that will have an audio interface built in. Like this one, but there also much cheaper ones but I'd be wary about their built quality. http://www.shure.com/americas/products/accessories/microphones/microphone-problem-solvers/x2u-xlr-to-usb-signal-adapter
If have you have an iPhone or an iPad if think there are pretty decent and affordable options available to connect a microphone with those devices and record them. Some of them might also work with the Macbook.
Yeah, I think the best thing to do would be to go to a local music shop and let someone show you all the available options. I haven't really followed the market on home recording in recent years, so there surely is a lot of stuff I'm not aware of. Just don't let them tell you that you need to spend hundreds of dollars just to get decent recording quality
Also I'm pretty sure there are bunch of youtube videos around showing you how to choose and setup for your very common use case