The easiest way to check is to grab a smartphone or tablet and go to your blog's home page. Is it hard to read -- are you seeing more of the left sidebar than the posts themselves?
Other ways to check: go to websites like TestiPhone.com or iPhone tester to see how things look on a smartphone's small screen.
If the blog looks wonky, call your webmaster and get this fixed.
For most blogging platforms, it's an easy fix. Wordpress has a plugin that solves the problem; Blogger does it automatically. (Blogger also provides its own preview for how Blogger blogs look on these smaller screen devices.)
Why should you care what device is used to read your blog?
Don't get overwhelmed. The biggest hurdle here is taking the time to check the blog's appearance on various tablets and smartphones; changing things to accommodate the smaller screen is simple to do.
It's an important task to undertake as soon as you can, though: it's estimated that more readers are going to be reading blog posts on smartphones and tablets than desktops and laptops very soon (think weeks or months), so getting your blog adapted for those smaller screens is a priority.
BOTTOM LINE? A hard to read blog post on a smartphone may remain an unread blog post -- and your time and effort in creating those blog posts deserves better, so make it easy for the smartphone reader to pull up and read what you've written.
For more, check out Forbes' article, " Smartphones, Tablets, Tab-Phones Edging PCs Off The Shelf?" and Econsultancy's take on things in "Smartphones and tablets: five key differences."
Even more? Read this piece written back in 2011 on Wikipedia, where Wikipedians are pondering where most of their readers are reading Wikipedia articles then (2011) and where those readers are going to be reading Wikipedia articles in the future.