As has been pointed out, "order" is simply being used to indicate the channel has requested or plans to make the series being referenced.
"Fox has ordered a full season of Gotham after test audiences provide
glowing feedback for the first episode."
Basically, this is indicating that Fox only produced at least the pilot episode and maybe a few others, but after seeing positive feedback from test audiences, they decided to make, or "order", a full season.
As such, ordering a show is simply referring to the studio requesting a certain level of production on a show. Think of it like the show is a burger at a restaurant, and you're the studio that walks in and says, "I'll order that burger."
Sometimes they'll use the phrase "green light" as well. This is referring to traffic symbols, so saying they've given something the "green light" means they've given it permission to move forward into production, the same way a green light at a traffic stop allows cars in that lane to move forward.
Now, to your question about why some shows are picked up for a full season all at once, and why others are ordered in batches of episodes. Basically, sometimes the studio isn't so sure a particular show will perform well, and as a result they only order a handful of episodes instead of a full season. Sometimes they'll "order" a full season after that if the first few have proven to do well, or they'll simply order another batch of episodes to continue to see how it does, or to provide closure to the story being told before canceling it. Should the show not perform as well as they'd like, they've only sunk money into, say, 10 episodes instead of a full season of (typically) 22 episodes, and can then put another show in the now canceled show's time slot to hopefully generate more ad revenue for them.
All of this comes down to the business end of the studio. They need to sell ads to make money, but they can't spend more on a show than they generate in ad revenue otherwise they'll lose money. Therefore they need to figure out which shows will do well before paying for an entire season. Sometimes they're not entirely sure how well it'll do, but want to give it a shot, and will therefore order a handful of episodes to start, and see where it goes from there.