Like many other types of social networking, Guest Blogging exposes you (in a good way, not that "scare-the-kids-and-get-carted-off-to-jail-in-handcuffs" kind of way) to the readers of the travel blog hosting your article, thereby helping to grow your audience.
In the process, by promoting (on your travel blog) your Guest Blog Post that's been published on the other travel blog, you're letting your readers know about that site and helping them to grow their audience as well.
It's a 'win/win' for both of you.
A good quality Travel Blog should - at the very least - give guest bloggers a link back to the guest blogger's travel blog as part of the article's meta data (author info at the end of the post), and often they will allow additional guest blogger info such as a photo, a biography, and social media links so that you can get new Twitter followers and/or Facebook friends and fans.
Tips for being a Good Guest Blogger: If you've been invited (or are offering) to submit a guest blog post, be sure to do the following:

• Do your homework - read some of the posts of the travel blog you'd like to write for to get a feel for what types and styles of articles they normally publish.
  If they have guidelines for submitting articles, read them;
• Ask if the blog owner has a specific topic in mind for your Guest Blog Post, and offer a couple of topic suggestions in case they don't or are just open to ideas;
• Ask how many words they would like, and if they'd like you to provide images as well (be sure that the images are your own or are royalty-free);
• Understand that your blog host may do some light editing (usually only styles such as bolding and italicizing words and phrases, adding paragraph breaks, etc) but if they do wind up correcting things such as spelling and grammar, be grateful - it keeps you looking good!;

Tips for being a Good Guest Blog Host: If you've invited someone to submit a guest blog post to your travel blog, try to keep this advice in mind:

• If you have a specific story topic or perspective you'd like, say so.
  If not, be open to suggestions;
• Keep your readers in mind - what would interest them? Realize that sometimes it's good to break out of your normal realm;
• Try to keep your copyediting to a minimum - after all, every travel writer has their own 'voice' and you don't want to stifle that;
• DO make corrections if you find spelling or grammar errors - you want your guest bloggers to look good to your audience - but it's nice to ask beforehand if your guest blogger minds such edits;
• Incentivize guest bloggers! Give them the ability to draw readers to their own travel blogs by displaying a link to their site in your post meta section, and if your WordPress Theme has an Author Template (author.
  php) use it to your guest blogger's advantage by including their photo, bio, and additional links;

The Travel Blogger community is one of the strongest and most supportive out there, and a Guest Blogger relationship benefits both the guest blogger and the hosting travel blog, so take advantage of any invitation that you receive to submit a guest blog post to other travel blogs or travel related website.
 In addition, you should also be actively seeking such opportunities, and offering to write for other travel blogs as well.