This post about wandering monsters that I made back in 2013 remains the single most popular post I have ever made to this blog (over 17,000 views and counting). It crops up all the over place - Web DM has an episode that discusses it, here's someone posting it to Stack Exchange, and a link to the post has shown up on Reddit about once every two weeks for years now (example). Someone else started calling it the "encounter grid" a year or two and the name seems to have stuck.
In the nearly six years since that post, I've done a fair bit of experimenting with encounter grids, and have made some changes to how I use them. I thought it might be worthwhile to some of the insights I've had about it since then.
The first insight is that I reversed the order of entries so the monster is more likely to show up the higher the roll is. I also changed some of the categories. It now looks like this:
1 - Traces
2 - Spoor
3 - Tracks
5 - Monster
6 - Lair
In the old version, results of 5 and 6 were both "traces", so this has more variety and more clearly communicates that proximity is the value measured by this axis of the grid. Also, my official word on the subject is that if the PCs roll "noises" you have to act the noises out.
This rearrangement of numbers lets you use this more easily as an ersatz tracking mechanic - the PCs decide to search for a monster or enemy for a period of time (e.g. a watch), you roll 1d6, and that's how close to the beast they've gotten (I would then push them to come up with diegetic ideas to close the remaining gap). You might allow them gear or abilities that add small bonuses (+1 or +2 tops) to this roll when they're tracking, which should integrate smoothly with the way other gear and abilities add bonuses to rolls.
The second thing I encourage you to experiment with is to list more than just monsters on the encounter grid. I wrote this post about using a similar style of encounter grid to generate traps a few years ago. If you stick traps on the same grid as monsters, I suggest you reinterpret the categories slightly - tracks might be warning signs of the trap's operation, while a lair result means you discover multiple instances of the same trap in close proximity (this preserves the maximum die roll as the result with the greatest risk). Beyond traps, feel free to insert environmental obstacles requiring increasing difficulty and risk to overcome.
A third thing is that with an encounter grid that lists aspects or elements of the monster beyond just its existence, you can start repurposing your encounter grid for other uses. Need a simple fetch quest or bug hunt? Need a component for a magic item? The encounter grid lets you easily generate these things. I also use it when I'm restocking dungeons, where it creates a heavily-traveled in, almost palimpsestic dungeon that has lots of evidence of monster inhabitation.
A fourth experiment is to consider using a d8 instead of a d6, but with the bottom two entries as blanks or nulls. The table then reads:
1 - Nothing
2 - Nothing
3 - Traces
4 - Spoor
5 - Tracks
6 - Noises
7 - Monster
8 - Lair
I suggest this for a couple of reasons. First, in my game Into the Depths, when you're doing things like tracking people, you only roll a d6 if you're doing it yourself, but you roll a d8 if you're helping one another out. So this means tracking as a group instead of a single person is rewarded: You still roll the d6 as a lonesome individual, but without a bonus (from clever thinking, gear, a specialised tracking retainer, etc.) you'll never find the monster on your own. So it encourages team-work amongst the PCs to hunt down beasts.
From experience, I have found that rolling every turn as a regular part of a site exploration procedure is easier to remember than rolling every other turn or every third turn. Adding a few null results makes that easier on the players by spacing out encounters. The chances of a monster encounter of some sort (i.e. the Monster or Lair results) reduce from 1 in 3 to 1 in 4 using this method.
As an additional aid, it helps distinguish which die is which, since rolling 3d6 and picking one out either requires a die of a different colour, or a lot of trust in one's players (I have them roll the dice for wandering encounters). Having one die be a different type reduces the chances of a misunderstanding or misreading of the dice.
These are some of the tweaks and expansions I've made to the system over the years. I encourage you to experiment with them yourself and see how they work for your table.