A Universal Translator requires computers capable of Natural Language Parsing (Processing).
A natural language parser attempts to deconstruct/parse a natural human language into an abstract language neutral form and then process that for meaning. Once it knows what has been communicated, it searches its database for a translation into the target language. To an extent something like this is already done for documentation that must be produced for multiple languages. A special XML language (usually SGML or something like it) is used. Different tags are used to denote the same section but in a different language. When "loading" the document, you specify the tags to use (e.g. Spanish) and the document's Spanish version of the sections are rendered so the user only sees those. But current SGML document construction is not done automatically - instead it is done by people, but processed by machines.
Writing code to deconstruct a language so that a computer can understand it and then match that with an expression construct from another language has been a sort of Holy Grail of language processing for decades - and it is a very tough problem.
Up to the 1980s, most NLP systems were based on complex sets of
hand-written rules. Starting in the late 1980s, however, there was a
revolution in NLP with the introduction of machine learning algorithms
for language processing. This was due to both the steady increase in
computational power (see Moore's Law) and the gradual lessening of the
dominance of Chomskyan theories of linguistics (e.g. transformational
grammar), whose theoretical underpinnings discouraged the sort of
corpus linguistics that underlies the machine-learning approach to
language processing. Some of the earliest-used machine learning
algorithms, such as decision trees, produced systems of hard if-then
rules similar to existing hand-written rules. However, Part of speech
tagging introduced the use of Hidden Markov Models to NLP, and
increasingly, research has focused on statistical models, which make
soft, probabilistic decisions based on attaching real-valued weights
to the features making up the input data. The cache language models
upon which many speech recognition systems now rely are examples of
such statistical models. Such models are generally more robust when
given unfamiliar input, especially input that contains errors (as is
very common for real-world data), and produce more reliable results
when integrated into a larger system comprising multiple subtasks.
BOLDED section is of special importance.
We have switched to the introduction of a very narrow type of AI (artificial/machine learning). It means that with enough study and processing power and Star Trek style Universal Translator might one day be possible but it could probably not work as quickly as that shown in the movies.