When we are looking at art we typically have an initial response or impression. This response to what we see (or hear, etc.) is formed by a lifetime of knowledge and experience and the culture and time in which we live. The expression “Beauty lies in the eye of the beholder” gets at the subjective and personal nature of perception—and of the “first impression,” in particular. There’s nothing wrong with one’s first impression or response—it is, after all, a personal response. It’s your point of view.
Formal analysis is a close and analytical way of looking at and discussing a work of art. It includes describing the work in terms of various elements, such as color, shape, texture, line, lighting, mass, and space, as well as a discussion of how those elements have been used (the design principles). Formal analysis moves beyond description of the artwork and its content by linking the elements of the work to the effects that they have on the viewer. This is discussion of the artwork from the point of view of “here is the artwork, and this is what I see and can make sense of . . .” Formal analysis uses art terminology to consider the effects of an artwork on the viewer (you), and it’s a process that enables us to think about and consider the overall meaning of the artwork.
The following video from the Getty Museum may help with your basic understanding of formal analysis:
Content is simply the the subject matter of an artwork. It’s the images you see—like the trees in a painting of a forest, or the town, the sky, and the moon in Van Gogh’s Starry Night. Content can play a role in formal analysis, but the content aspect is less important than the “artwork” aspect in a formal analysis. A contextual analysis, however, often brings additional information to light allowing a deeper appreciation beyond the formal (visual) aspects alone.