If you open your local install of PHPMyAdmin and click first on the database you wish to export on left menu we'll call it
myphotos for example, over on the right side, top of page you'll see a tab titled Export. Click that. On the page that opens you see many options. To understand them all, the docs is the best way to go.
For the basics, you could try this. In the Export column click the "Select All" option which will highlight all your tables in this database. Down below leave SQL ticked.
To the right of that you see the Structure settings, these could be left to default. That is unless you plan on updating this data using the same database. If so then tick the Add DROP TABLE option. When you upload this table to your online database, if tables already exist they will be dropped recreated and populated with the new data from this SQL backup you're about to make.
Down at bottom of page you see the section to Save as File. Tick the Save as File, Untick the Remember Template name and type a name in,
myphotos, as an example here, also tick gzipped to compress the file if large. If not leave set to none.
Now click the Go button, bottom right corner and save to desktop.
Depending on your selection of Save File, you should now have either a file named myphotos.sql.gz or myphotos.sql The first of course is a compressed version of the second.
Now you want to add it to a database on your cPanel server. But, you need a database setup first. I just posted some comments on this sort of thing to another thread you might find useful here:
http://forums.cpanel.net/f34/loading-joomla-site-138977.html#post595825
Or there's a cPanel training video you might watch here:
Add MySQL
Now you have a new database created, and a backed up SQL file on your desktop that you want to upload to the server.
Open PHPMyAdmin on the server, find the newly created database here on left menu and click title. On right side of page, at top find the Import tab and click. Here you'll see the Browse button for Location of Text File section. Click that and point it to your myphotos.sql on desk.
Now down bottom of page click the Go Button.
If all goes well, the database will be imported to the server.
This is of course very generalized to be sure, but should give you some idea of what needs done to accomplish what you seek.
That said, if you like working with databases this is one way to go. If you just wanted to get a bunch of photos online to that website, there are plenty of easier ways to do this. Uploading a gallery of some sort might be one of the easiest.
Or even easier yet, use a free tool like
flikr or
Picasa or even something as dead simple as this one,
Web Gallery Creator, where you set a few options, point it to your images, and click Create Gallery. Everything is sent to a new directory and a gallery is created for you. Upload that directory to your site, customize it a bit and you're done.
This forum isn't really for this sort of support though, please keep that in mind. If you have problems with your cPanel and using PHPMyAdmin, you'll do best to ask your host for support. For more on using PHPMyAdmin on your home server, the docs for it should be checked out.
Not sure if that helps much, but there you go. :p
Good Luck.