Put simply, 'Alt Text' means 'Alternative text for images'.
It is an attribute you can (and REALLY SHOULD) apply to any image on your website. It allows screen reading software (like Chrome Vox or Fire Vox) to describe the image to the blind person who is visiting your site.
So this image:
Has Alt Text that says "Picture of lemur sitting on a log" because that's what the image depicts.
How do I check to see if an image has Alt Text?
Using Chrome or Firefox (I simply can't be bothered to explain how to do this in Internet Explorer, use Chrome or Firefox!) move your mouse over the image you want to check, then right click it and choose 'Inspect Element' from the drop down menu.
You should see some code that looks like this:
Basically anything in this set of inverted commas: alt=" ... " is the Alt Text.
How do I apply Alt Text to an image?
If you're using a Content Management System (like WordPress or similar) you can normally click on an image (once you've uploaded it to a web page), go into the image attributes and there'll be a space for Alt Text:
If you're not using a CMS, you need to make a list of all the images on your site, write some relevant Alt Text for each one and ask your web designer to add it to each image.
How do I use Alt Text for Search Engine Optimisation?
Very carefully! The primary purpose of Alt Text is to describe the image to blind users.
Google has historically been pretty bad at seeing images, so it has relied on Alt Text to get a deeper understanding of what is on a page. Knowing this, you can exploit Alt Text a little by using images on your page that are of the product or service you want to sell and using the phrase you want the page to rank for in the Alt Text of any images on that page. You can read more about optimising your site for search engine's on this page here.
Please don't abuse Alt Text as it will make your website less useful for those with poor eyesight and will probably result in Google considering your site as a bit spammy, which may result in a loss of ranking and a loss of traffic.