What is mixing?

Mixing is simply the combination of sounds that is professionally blended together to accomplish a balance.

Recording is the most important stage of Audio Production, being followed by Mixing, then Mastering. 

What is mastering?

This is the third most important step in Audio. This is the final polish of the product. Many engineers say this is a "dark art" that is subjective to each person. 

Mastering adds consistency to the album by increasing the dynamic range of each project. 

"So if It's subjective, can I master my own stuff to my taste?" According to Sound On Sound you should not do your own mastering and here's the reason why;

"Maybe you have a live recording that you want to give to friends or sell at gigs. Sure, you can just duplicate the mixes, but a mastered 'veneer' will give your listeners a better experience. Or perhaps you've recorded several tunes and want to test how they flow together as an album. Why not master it yourself? After you've sorted out the order and such, you can always take the individual mixes to a pro mastering engineer. And when you do, you'll be able to talk about what you want in more educated terms, because you're more familiar with the process, and you'll have listened to your work with mastering in mind.

Besides, the only way to get good at anything is practice. For years, I used only professional mastering engineers; I would never have dreamed of doing mastering myself. But I learned a lot from observing them, started mastering my own material, and now people hire me to master their recordings because they like the results I get. Still, if you have any doubts whatsoever about your abilities, seek out a professional who can present your music in the best possible light.

Most mastering is done with specialised digital audio editing programs such as Sonic FoundrySound Forge, Steinberg Wavelab, Bias Peak, Adobe Audition, and so on. These offer good navigation facilities, the ability to zoom in on waveforms, pencil tools to draw out clicks, and plug-ins for mastering tasks (along with the ability to host third-party plug-ins). However, if your requirements aren't too demanding, there are several ways to master using conventional multitrack recording programs. And, interestingly, some can even do tricks conventional digital audio editors can't."

Article source: https://www.soundonsound.com/sos/aug04/articles/computermastering.htm