"A taxi" uses the indefinite article "a," so "a taxi" could
refer to any taxi. "The taxi" uses the definite article "the," and
therefore it refers to a specific taxi.
Examples:
"I will take a taxi to the airport." -- This means you do not
yet know exactly which taxi you will take.
"I will take the taxi to the airport." -- This means there is a
particular taxi that you plan to use, such as the one across the
street, taxi #34, the taxi that you have already requested to come
pick you up, etc.