Structuring a JSON array with objects
I think I would replace { resize: [1200, 1200] } with { operation: 'resize', parameters: [1200, 1200] }. This is more verbose, but easier to maintain/read. This way it's eligible for extension (maybe you want to add identifiers later?). The same can be done for the tasks.

Other than that there's not a lot to say. I find the indentation not easily readable, but that's just style. I'd prefer:

[
    {
        name: "I'm task one",
        operations: [
            {
                operation: "resize",
                parameters: [1200, 1200]
            },
            {
                operation: "moveTo",
                parameters: ["dest/nick"]
            },
            {
                operation: "rename"
                parameters: ["{base}-12.{ext}"]
            },
            {
                operation: "toWeb",
                parameters: [true]
            },
            {
                operation: "rename",
                parameters: ["{base}.{ext}"]
            }
        ]
    },
    {
        name: "I'm task two",
        operations: [
            {
                operation: "resize",
                parameters: [1000, 1000]
            },
            {
                operation: "rename",
                parameters: ["{base}-10.{ext}"]
            }
        ]
    }
]


Also note that the value of the parameters is an array, even if it has one value.