Complete protein, in a nutshell, is protein that contains the 9 amino acids that the human body cannot create on its own. Amino acids are important because they are what builds protein strands. You ingest a food containing the 9 essential amino acids, your body rearranges the amino acids in strands of protein which build muscle and connective tissue.
Myth: Plant based protein is lacking in 9 essential amino acids
Fact: Every plant based food contains all 9 essential amino acids! Yes, you read that right. However, each of the foods on their own do not all have the right levels of amino acids for ideal muscle growth, which is why eating a varied (plant based) diet throughout the day is important, especially if attempting to gain extra muscle. This does not necessarily mean that you need to combine proteins at each meal. Your body takes the amino acids ingested and creates little reserves so that it can mix and match the proper proportions of amino acids at a later time to create new proteins. So basically, as long as you are eating enough healthy calories, it is very difficult to be deficient in complete protein. Your body is smarter than you think!
Bonus Fact: the ONLY food source (plant based and animal based) that is not complete is gelatin.