The complexity of the model and the expected time to complete it will increase with the recommended age.
Lower aged sets, like the Juniors line, feature builds that rely heavily on standard stacking and more basic bricks.
As the age recommendation goes up, you'll see more advanced building techniques such as offset stacking (think stair stacking), studs not on top (SNOT technique), thinner walls (think 1x4 instead of 2x4), more plates instead of just bricks, and more.
Sets for younger children are also designed for the type of play those ages engage in. And they tend to feature brighter, primary colors, which also appeal to those age groups.
Looking at set 10672, LEGO Juniors Batman: Defend the Batcave, we can see evidence of these things:
- The set uses large pieces for structure, which is a very basic and easy technique.
- The set features a car, the Batmobile, which is low on detail but structurally will hold up to the more rough play of 4-7-year-olds. Cars are very, very common for these types of sets
- The set is very open, so it's easy to access from many angles for an age range still developing motor control
- We see a lot of bright colors, including a blue Batman instead of a black or earth (dark) blue Batman suits we normally see
Now, we can contrast this with a slightly higher age range set, 75099 Rey's Speeder.
The Batman set was ages 4-7, and this Star Wars set is ages 7-12:
- The Star Wars has more pieces, 193 vs. Batman's 150
- The set itself is smaller in size, because it makes use of smaller pieces (which require more fine motor control to properly place)
- The set does not come with a play area, although that's not always the case
- The speeder itself features the sideways building techniques, where the tops of the elements don't point up
- The color scheme is more muted, featuring dark reds and and more grays, although this is also common with licensed sets
You won't necessarily be able to apply these attributes universally across sets, especially since the age-ranges sometimes overlap, as seen in 60043 Prisoner Transport, which has an age range of 5-12.
None of this is to say that younger kids can't assemble and enjoy older-ranged sets, but the ranges given are typically where the most enjoyment and least frustration will be found.
Something else you won't see on the box is the difference in styling of the building instructions. For the Batman set's (PDF), we see there's only a single task per page, and they're often broken down into smaller steps or have large, clear arrows indicating placement. In the Star Wars set's (PDF), we see that each page has two numbered tasks and placement is less likely to be indicated by arrow for simple tasks.
These differences in instructions are because of the expected abilities and attention spans of the intended audiences. Again, this is to reduce frustration and enable the children to be more successful building the sets without relying too heavily on the adults to help.
The LEGO company does a lot of research into what types of play are better for children at different ages, because it gives them a better product. You can seem some of the information they provide parents about types of play on their Parents website, and more involvement with child education from their LEGO Education company.
This answers comes from my experience as a consumer of LEGO product for different age ranges and as a previous customer service representative. I was asked questions about the recommended age ranges on a weekly basis, and the answer I provided to customers was similar to the answer here.