What information does the summary line contain?
inet.0: 736608 destinations, 806660 routes (736608 active, 0 holddown, 7 hidden)
A JunOS router imports routes into one or more routing tables. inet.0 is the main routing table for IPv4 routes. Its IPv6 equivalent is inet6.0. Routes from all routing protocols and statically / connected routes are collected in these tables. Juniper has more information about routing tables on their site.
The destinations number is the amount of unique destinations the system can reach. Right now we have around 740k of routes in the global routing table (the Internet) so this number is about right.
The amount of routes is the number of... well... routes the system can choose from to reach a destination. In your case it's not a lot more (maybe you have an upstream which gives you a full table and an IXP/peering port) but for example if you have two upstreams this number will be twice the number under destinations because the router knows two routes for each destination reachable via the two upstream providers. So in short: A router can possibly reach a single destination over many routes.
active routes are routes that are currently deemed the "best path" for a route by the router and so these are installed in the forwarding table of the router and used for traffic forwarding.
holddown routes are routes that were active before but for some reason are no longer active. The router keeps them in the routing table a bit longer if some process needs them. If no process has any more interest in these routes they are removed completely.
hidden routes are routes that were rejected by routing policy or other mechanisms on the system. You can show what routes are hidden in the table by using show route hidden table inet.0.
What does Active, Last Active and Both mean?
As said a router can have multiple routes to a destination. Normally it will choose the "best path" and this becomes the active route/path. If this best path changes for some reason the "old" best path becomes the Last Active and the new best path becomes the Active route. After a while it will be Both again. (I'm not 100% sure when that happens but it is a relatively short time.) In your example the first route is the best and so it has an asterisk in front of it.
What does the number 170 besides BGP mean?
This is what Juniper somewhat ambiguous calls "Route Preference". I would rather call it Protocol Preference. Other vendors call it Administrative Distance. It simply means in which preference routes from different routing protocols are evaluated in the routing table. Routes for a destination learned from a routing protocol with a smaller number (connected and static routes are routing protocols as well) will be used in preference of routes learned from a protocol with a higher number. For example BGP has a preference of 170 while static routes have a preference of 5. So whenever you have a destination that is reachable either by a route learned from BGP and a static route the static route will be the better one. All route preferences are listed on the Juniper Website.
What's the difference between route preference and BGP local-preference?
Route preference gets evaluated first. This decides which routing protocol will be preferred if both have information for the same destination. If the router must choose between two routes learned by BGP (and so route preference is the same) local-preference is evaluated (among other metrics) to choose the best path to the destination. Juniper lists this decision process on their site as well.
What does the I at the end of the as-path mean?
The letter at the end of the AS-Path stands for the BGP origin information. It has three possible values:
I - Route was learned from an IGP at the origin ASE - Route was learned by EGP at the origin AS (This should never be used)? - Route origin is unknown by the origin AS
This setting is freely configurable by the origin AS and has no real connection to how the route was actually learned there.
