Every H tag represents a title, sub-title or an ordered/unordered list or sub-list.
H1 would be your post title.
H2 for the section title.
H3 for a sub-section.
H4 for a list of things.
The <h1> tag is the one that Google gives top priority to and is the title of your post/page. And it's the #1 SEO signal to a Search Engine as to what the post/content is about. If you want to rank for that keyword, you need it in the <h1> title! Every post/page should have an H1 tag as the title and should only use it ONCE on that page. Any more than that and you could get seen as keyword stuffing.
The <h2> tags are your sub-headings in your post/page. Search Engines look at the keywords within these tags also. And you get SEO points for using your keywords within your <h2> sub-headings.
The <h3> tags are also for sub-headings. But in a much smaller font size so carry less weight in terms of SEO. But they're still worth using to make your post/page look nice and organized which benefits your readers and your website's appearance too.
The size of the H1 tag is set by the styling rule that's applied to it in your CSS file. Some WP themes have theme options which let you change the size of the H1 title. Or, you can just find it within the CSS file and then change it yourself.
See this H1 CSS styling example, for example. You should not use an H1 tag simply because it's too big. If it's too big, then you should adjust the font size using your themes settings, or manually yourself in the CSS file.
An alt tag, also known as "alt attribute" and "alt description," is an HTML attribute applied to image tags to provide a text alternative for search engines.