'Internal' and 'external' criticism are rather dated terms to refer to a theoretical division of source criticism. The terms enjoyed a brief vogue in handbooks beginning in the early twentieth century and persisting until the 1960s, where they were used as synonyms for the older terms 'higher' and 'lower' criticism. They persist as vestiges in other fields (such as the social sciences) which draw in part on historical studies for their method.

The idea of source criticism, that the historian should establish how and why an extant source (usually conceived of as a text) has survived and what that source means by careful examination of both its form (what the physical document looks like, sometimes known as 'diplomatics') and by careful reading (to establish the reliability of its account being a main aim), became a major concern for historians in the nineteenth century. It was perceived as perhaps the most important technical skill that distinguished the professional academic from the pre-modern historian.

Today source criticism is still recognised as a central and important part of historical practice but as a much smaller part of the process of historical interpretation, and is not easily divisible into parts (because the range of sources is much larger and techniques for an archaeological site, a coin, and a document, are very different). But in the early twentieth century this was seen as a useful division by some practitioners.

'External' or 'lower' criticism is the more clearly defined. It refers to the physical examination of a manuscript, primarily to establish its authenticity but also to ensure an accurate reading (for example, where a word is unclear). By contrast 'internal' or 'higher' is often rather vaguely defined in handbooks. It pertains to the reading of that text, perhaps conceived as recovering the intended meaning, or detecting bias, or establishing reliability (the last of which presumes not only a text but a text which is descriptive, such as a pre-modern history, in character).

I would not use these terms today, other than as a hook for a lesson on historiography. If you want to teach source criticism there is no reason for such a subdivision, it needlessly replicates a logocentric and positivist nineteenth century conception of historical practice.