When we say that base malts are the foundation of a beer, we mean that they will contribute the bulk of the sugars for the yeast. They usually make up most of the grist, and they supply enough enzymes to convert their own starches as well as those of any additional specialty grains or adjuncts.
At a high level, three factors differentiate these malts: modification, diastatic power, and color. Modification refers to how accessible the starches are within the kernel. Today, most brewing malts are well-modified, meaning that the maltster let the kernel sprout long enough to start breaking down the barriers to accessing the starch. Earlier in brewing history, malts were much less well-modified, so multistep mash processes were developed to assist things.
Diastatic power defines how much alpha and beta amylase the grain provides, which determines how effectively it will convert its own starch along with that of any adjuncts or specialty grains. (Recall that alpha amylase chops long starch chains up and beta amylase nibbles the ends into fermentable sugars.) A base malt with lower diastatic power, such as Vienna malt, will still be able to convert its own starches, but it might be challenged by larger percentages of non-base malt.